An article at MSNBC talks about the controversy of pilots sleeping while in flight.  The discussion about airline pilots is a separate issue; the article specifically mentions military pilots, however:

Even a 10-minute nap can improve a pilot’s performance, said Scott Shappell, a Clemson University professor who as director of the Human Factors Institute helped write the flying policies that govern military pilots.

In the military, pilots flying alone have been allowed for decades to take naps, Shappell said. “I can tell you absolutely, but good luck trying to find proof of this, in the military we have single-seat pilots take naps,” he said. They’re called ORPs – officer rest periods – and last from 10 to 20 minutes.

Shappell doesn’t cite his source (he is cited as an expert) and downplays the ability to support his assertion.  There is probably good reason there’s no “proof” of his claim that single seat pilots sleep at their controls.  If they did, those pilots are probably grounded or dead.  As an example, AFI 11-202v3, the Air Force Instruction governing flight operations, says this:

9.9.6. Controlled Cockpit Rest. Unless further restricted in a MAJCOM Supplement or MDS specific Volume 3, controlled cockpit rest may be implemented when the basic aircrew includes a second qualified pilot.

Unless Shappell figured out how to squeeze a second pilot into a single-seat plane, there’s no way an Air Force pilot could legally do what he suggested.  (The Navy?  They have their own rules…)  In addition, it is noteworthy that Shappell didn’t explain how those single-seat pilots would be woken up.

While aircraft with multiple aircrew may indeed have sleeping pilots, a more accurate answer to single-seat pilots and rest may be the development of the sometimes controversial “go pills.”  Rather than let them sleep (would you sleep in your car by yourself barrelling down the interstate?), they’ve given them drugs to keep them awake.